$a_n={n\left(\dfrac{5}{4}\right)^{2n+1}}$ 1) Find $\lim_{n\to\infty}\left| \dfrac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left|\, \frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=$
Explanation: $\lim_{n\to\infty}\left| \,\frac{{{a}_{n+1}}}{{{a}_{n}}} \,\right|=\dfrac{25}{16}$ Since the limit, $\dfrac{25}{16}$, is greater than $1$, the ratio rest tells us that the series diverges.